Alias - Revision history

Harrde at 21:18, 11 November 2007

2007-11-11T21:18:01Z

← Older revision		Revision as of 14:18, 11 November 2007
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	The figure above shows that if the original signal (black) is not sampled fast enough ~~than~~ another signal (blue) can be incorrectly "recovered" which passes through all the sampled points but is clearly not the same as the orignal signal. This incorrect signal from aliasing has correct frequency components for those components which are lower then half the sampling frequency. The components which are higher than half the sampling frequency end up with frequencies equal to the original signals' frequency components minus the sampling frequency.		The figure above shows that if the original signal (black) is not sampled fast enough then another signal (blue) can be incorrectly "recovered" which passes through all the sampled points but is clearly not the same as the orignal signal. This incorrect signal from aliasing has correct frequency components for those components which are lower then half the sampling frequency. The components which are higher than half the sampling frequency end up with frequencies equal to the original signals' frequency components minus the sampling frequency.

	It should be noted that other signals can be found that pass through each of the sampled points, but their incorrect frequency components will all have frequencies higher than the original signals' highest frequency components. Thus, they can ~~and should~~ be filter out by a low pass filter.		It should be noted that other signals can be found that pass through each of the sampled points, but their incorrect frequency components will all have frequencies higher than the original signals' highest frequency components. Thus, they can be easily filter out by a low pass filter.

Harrde at 21:16, 11 November 2007

2007-11-11T21:16:23Z

← Older revision		Revision as of 14:16, 11 November 2007
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	The figure above shows that if the original signal (black) is not sampled fast enough than another signal (blue) can be incorrectly "recovered" which passes through all the sampled points but is clearly not the same as the orignal signal. This incorrect signal from aliasing		The figure above shows that if the original signal (black) is not sampled fast enough than another signal (blue) can be incorrectly "recovered" which passes through all the sampled points but is clearly not the same as the orignal signal. This incorrect signal from aliasing has correct frequency components for those components which are lower then half the sampling frequency. The components which are higher than half the sampling frequency end up with frequencies equal to the original signals' frequency components minus the sampling frequency.

	It should be noted that other signals ~~with~~		It should be noted that other signals can be found that pass through each of the sampled points, but their incorrect frequency components will all have frequencies higher than the original signals' highest frequency components. Thus, they can and should be filter out by a low pass filter.

Harrde at 21:06, 11 November 2007

2007-11-11T21:06:51Z

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	==Aliasing==		==Aliasing==
	The Nyquist Theorem states that you must sample at a frequency which is twice that of the highest frequency components of the sampled signal in order to recover the sampled signal. If you sample at rate lower than this you get aliasing. Below is a figure which shows how aliasing occurs and the Matlab code for it.		The Nyquist Theorem states that you must sample at a frequency which is twice that of the highest frequency components of the sampled signal in order to recover the sampled signal. If you sample at rate lower than this, you get aliasing. Below is a figure which shows how aliasing occurs and the Matlab code for it.

	[[Image:harrdeH11Fig.jpg]]		[[Image:harrdeH11Fig.jpg]]
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	title('Aliasing: Signal With Frequencies up to 3.66Hz Sampled at 5Hz');		title('Aliasing: Signal With Frequencies up to 3.66Hz Sampled at 5Hz');
	</pre>		</pre>

			The figure above shows that if the original signal (black) is not sampled fast enough than another signal (blue) can be incorrectly "recovered" which passes through all the sampled points but is clearly not the same as the orignal signal. This incorrect signal from aliasing

			It should be noted that other signals with

Harrde at 20:54, 11 November 2007

2007-11-11T20:54:55Z

← Older revision		Revision as of 13:54, 11 November 2007
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	[[User:Harrde\|Back to my page]]		[[User:Harrde\|Back to my page]]

			==Aliasing==
			The Nyquist Theorem states that you must sample at a frequency which is twice that of the highest frequency components of the sampled signal in order to recover the sampled signal. If you sample at rate lower than this you get aliasing. Below is a figure which shows how aliasing occurs and the Matlab code for it.

	[[Image:harrdeH11Fig.jpg]]		[[Image:harrdeH11Fig.jpg]]

			<pre>
			clear all;

			Ts = .2; %Sampling time (s)
			ws = 2*pi/Ts; %Sampling frequency (rad/s)

			t = [0:0.005:2]; %Time vector

			w1 = 7; w2 = 23;
			y = cos(w1t) + cos(w2t); %Original Signal

			t1 = [0:Ts:2];
			xs = cos(w1t1) + cos(w2t1); %Sampled points

			w2s = w2 - ws;
			x1 = cos(w1t) + cos(w2st); %Signal from Aliasing

			figure(1); %Plot
			clf;
			plot(t,y,'k',t,x1,'r');
			hold on
			stem(t1,xs);
			hold off;
			legend('Original Signal', 'Signal from Aliasing', 'Sampled Points');
			xlabel('Time (s)');
			ylabel('Amplitude');
			title('Aliasing: Signal With Frequencies up to 3.66Hz Sampled at 5Hz');
			</pre>

Harrde at 20:44, 11 November 2007

2007-11-11T20:44:50Z

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	[[Image:~~Example~~.jpg]]		[[Image:harrdeH11Fig.jpg]]

Harrde at 20:42, 11 November 2007

2007-11-11T20:42:18Z

← Older revision		Revision as of 13:42, 11 November 2007
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			[[Image:Example.jpg]]

Harrde: New page: Back to my page

2007-11-11T19:58:41Z

New page: Back to my page

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